First of all, thank you for looking into this! We really appreciate it!
Secondly, I wanted to show an example of the error we are having with the tests:
If you run the following code in Jupyter notebook or just a normal python script, the image generated by fig.savefig() and plt.savefig() will look like this:
Code:
fig, axs = plt.subplots(2, 2,
subplot_kw={"xlabel": "x", "ylabel": "",
"title": "Title"})
axs[0][0].imshow(plt.np.zeros((5, 3)))
axs[0][1].imshow(plt.np.zeros((3, 5)))
axs[1][0].imshow(plt.np.zeros((2, 1)))
axs[1][1].imshow(plt.np.zeros((1, 2)))

axs[0][1].set_title('Title2', loc="left")
fig.draw_without_rendering()
fig.align_titles()
fig.draw_without_rendering()
fig.savefig("fig_align_titles.png")

Generated image:

The problem we are facing now is, that the image generated by pytest when fig.savefig() is used looks like this:
Image generated by pytest:

When align_labels() is used though, the labels in images generated by pytest do show aligned labels. We are not sure what else we should do.

The tests use the "classic" style by default. For copying on recent matplotlib, I think plt.style.use('classic') should look the same.

Is the 'classic' style rendered differently then? Have there been known workarounds or solutions?

The test images were created before the new default style, so many older tests use the old style. https://matplotlib.org/stable/gallery/style_sheets/style_sheets_reference.html
We don't change the style so that we don't have to regenerate the images, which makes our repository larger and more unwieldily.

Since these are new test images, they should probably set to the new style by passing style="default" to the image_comparison decorator:

See this for an example:

@jklymak That makes sense. Thanks for clarifying.
@ksunden Thanks for pointing that out! I didn't know you could do that.
Is this an allowed approach? If that is the case, we would change the tests to use the 'default' style.

For new tests it is allowed, even encouraged. (Though if we can avoid image comparisons all together, that is even moreso encouraged... haven't looked too closely here to know how good such tests would be, and not too offended by more image tests, just they are a higher maintenance burden than non-image tests.)

It would be a big lift to change old tests, though, and that is why its the default still...

There have been talks about explicitly setting old style on all image comparisons where it is not explicit, then transitioning to newer style being default (and thus the case for all new tests) but that is a slow process.

https://matplotlib.org/stable/devel/testing.html#writing-an-image-comparison-test

Also actually the preferred key is "mpl20" which is just a stable alias for the current "default" style, such that if we change defaults again, the tests using it will retain current behavior. (It is currently just mapped to "default", and the similar alias "mpl15" is mapped to "classic")

Thanks the info, I really appreciate it! Then we will update the tests asap :)

FWIW, I think it's probably bad idea to have examples that are clearly broken in some respect - in this case with overlapping labels. Either manually make enough space with subplots_adjusts or some such, or use constrained_layout. In fact this should almost definitely get a test with constrained_layout.

@AlextheGreat1509 do you need help addressing the CI failures here?

Closing in favour of #27952.